4
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enter image description here

How do you find the phase and inverse Fourier transform of this frequency spectrum?

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    $\begingroup$ Is this a homework assignment? $\endgroup$
    – hotpaw2
    Commented Jun 23, 2014 at 19:15
  • $\begingroup$ no it isn't.... $\endgroup$
    – martinap
    Commented Jun 23, 2014 at 19:18
  • $\begingroup$ The spectrum is usually complex. Sometimes the definition implies "magnitude", which is real, but in that case it would be positive. Perhaps you could clear this up a little from the context of the book? In this meant to be a Fourier representation of a signal which happens to be purely real? $\endgroup$
    – Phonon
    Commented Jun 23, 2014 at 22:45

1 Answer 1

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  1. The magnitude is given by $ {\left| X \left( f \right) \right|} $ hence it is 6.
  2. Assuming all data is given in the graph, the function isn't complex it is only negative -> Phase is -180 degrees.
  3. You should use its symmetry. Without over thinking it, It could be generated by a window on the center convolved with 2 deltas (Shifted) -> Sinc in time multiplied by 2 exponentials.
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    $\begingroup$ The magnitude is $|X(f)|$, not $|X(f)|^2$ (which is the squared magnitude). So its value is 6, not 36. $\endgroup$
    – Matt L.
    Commented Jun 24, 2014 at 7:43
  • $\begingroup$ By the book you're correct. Yet usually this term is abused, and I assumed this to be the case :-) (Since otherwise it would be seem trivial). Anyhow, fixed it. $\endgroup$
    – Royi
    Commented Jun 24, 2014 at 7:48

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